Question

use the quotient rule to divide. then simplify if possible.\\(
\frac{\sqrt3{108}}{\sqrt3{4}}\\)\\(
\frac{\sqrt3{108}}{\sqrt3{4}} = \square\\)
(type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Apply the quotient rule for radicals

The quotient rule for cube roots states that $\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}}$. So we can rewrite the expression as $\sqrt[3]{\frac{108}{4}}$.

Step2: Simplify the fraction inside the cube root

Calculate $\frac{108}{4} = 27$. Now the expression becomes $\sqrt[3]{27}$.

Step3: Evaluate the cube root

We know that $3^3 = 27$, so $\sqrt[3]{27} = 3$.

Answer:

$3$